Problem: What do the following two equations represent? $x-4y = -4$ $16x+4y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $x-4y = -4$ $-4y = -x-4$ $y = \dfrac{1}{4}x + 1$ Putting the second equation in $y = mx + b$ form gives: $16x+4y = 3$ $4y = -16x+3$ $y = -4x + \dfrac{3}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.